Physics 120 Spring 2008 Problem Set 5 due Monday, April 7
cable
f
q
hinge
1. A concrete block of mass 200 kg hangs from the end of a uniform beam of mass 40.0 kg. A cable attached to the end of the beam keeps the system in equilibrium.
Physics 120 Spring 2008 Problem Set 2 due Wednesday, February 20 Use the problemsolving framework described in chapter C5 when writing solutions to the following problems. I will expect you to: (a) Translate the problem set up a coordinate s
(C5T.5) Two magnetic hockey pucks sliding on a flat plane of frictionless ice attract each other, changing each other's direction of motion as they pass. We can (or cannot) realistically apply conservation of momentum to this situation because (A) (B
IMPORTANT DEFINITIONS
displacement: velocity:
r
r lim t t 0
rf
v
ri dr dt
momentum:
p mv
dp A , where dp A is the impulse dt
force: FA
weight:
Fg
mg , where mag( g ) 9.8 N/kg
(based on C3B.1) An object is observed in a certain
Vectors
A vector quantity is a quantity with both a size and a direction Vector quantities are represented graphically by an arrow: the length of the arrow corresponds to the vector's size, and the orientation of the arrow indicates direction The
Suppose a system of particles experiences no external interactions. What else must be true?
(A) (B) (C) (D) (E)
It also experiences no internal interactions. Its total momentum is not conserved. Its center of mass is stationary. The system's total
Which of the following is the better explanation of what drives a rocket forward? (A) The rocket and propellant function as an isolated system. When the propellant leaves the nozzle it has momentum, and the rocket receives an impulse in the direction
The static and kinetic friction forces on an object are proportional to the normal force acting on the object
FSF s FN FKF K FN
Generally,
K S
A block rests on a rough floor. A horizontal force of 5 N is required to get the block moving. Once
Quiz 2 Checklist
degrees of isolation (floats in space, etc.) law of conservation of momentum types of energy (Kinetic, Potential) The Law of Conservation of Energy potential energy functions: focus on spring and gravitational potential energies
vi
h
vf = ?
The law of conservation of energy can help us calculate the speed of the ball when it reaches the ground, but it cannot tell us the path that the ball follows in getting there.
The basic rule that relates force to motion is Newton's 2
Forces are shown on three objects below. For each object, show and label the net force vector
The figure below shows a force vs acceleration graph for a single object of mass m. Force and acceleration data have been plotted as individual points at s
Quiz 4 Checklist
Newton's Second Law Third-law partners Motion diagrams Derivatives Free-body diagrams Graphical display of motion
Equations you should know:
vx ax Fnet
dx , etc. dt dvx , etc. dt ma
Macroscopic Interactions
Long-range
(ex., gravity)
Contact
(tension, compression, friction)
A ball swings back and forth on the end of a string. The ball interacts with the earth via the long-range gravitational interaction. The ball also interact
Blocks A and B are held in the palm of your outstretched hand and your hand is lifting the blocks at constant speed. Assume that mB > mA.
B A hand
B ( A) FN
A( H ) FN
TLP
B (E ) Fg
A(E ) Fg
A( B ) FN H ( A) FN
TLP
A(E ) A( B ) B (E )
Quiz 5 Checklist
The reverse kinematic chain (axvxx): graphical methods and calculus Objects in static equilibrium: forces and torques must sum to zero Static and kinetic friction
Equations you should know.
tf ti
x vx
v x (t )dt
tf
r F FSF S
Ceiling Wall
String
String
Suppose the block has a mass of 2-kg and the upper string makes a 30 angle with the vertical. What are the tensions in the two strings?
FT 2
30
FT 1
Fg
mg 19.6 N
Fg
FT 2 cos 30
FT 1
Fg
FT 2
19.6 N cos30
22.6
(C14T.6) If global warming proceeds during the 21st Century as anticipated, it is possible that the polar ice caps will melt, substantially raising sea levels around the world (and flooding coastal cities such as New York). Would this shorten, length
The dot product is one way of multiplying two vectors. Another way is the cross product, whose magnitude is defined by the relation
mag ( A B) AB sin
and whose direction is given by a right-hand rule.
Indicate whether the cross product of the t
Thermal Energy
U W Q
HEAT
Internal Energy
WORK
Internal Energy: Includes thermal energy; chemical energy; nuclear energy Thermal Energy: that part of the internal energy which changes when the temperature changes (note: typically, we measure tem
The dot product is a type of vector multiplication. The dot product of two vectors is defined by the relation
A B ABcos
If the vectors are expressed in terms of their components, an equivalent way of calculating the dot product is
A B Ax Bx
dr
R
d
If is measured in radians, then
dr = R d
Divide by the time interval dt:
dr/dt = R d/dt v=R
This is true only if is expressed in radians!
= "angular speed"; v = "rotational speed" or just "speed"
A rotating fan turns counterclockwise a
(C7T.3) The general gravitational potential energy formula, V(r) = - Gm1m2 / r, is always negative for r > 0, but the empirical formula V(z) = mgz is always positive for z > 0. Why are the signs in these expressions different? (A) The empirical formu
Projectile Motion
Simple Projectile: an object that moves in such a
way that g is constant (in magnitude and direction)
and air drag is unimportant.
Galileo’s Insight
“the …motion which I call projection
is compounded of one which is
uniform and horizon
Quiz 3 Checklist
dot product of vectors k-work angular velocity moment of inertia rotational kinetic energy the "no slipping" condition thermal energy heat vs work
Quiz 3 Checklist Equations to know
A B dK
I
i
AB cos( ) Ax Bx v dp F
vx
x
t
t
dx Since vx , the value of vx at some time t dt tells us the value of the slope of the x vs t graph at that instant.
Below are shown two velocity versus time graphs for objects moving along the x axis. Draw the corresponding position ve
Answers to Problem Set 2 Physics 120 Spring 2008
5 1. The initial speed of the alpha particle is 4.84 x 10 m/s. Its speed after the collision is 5 4.15 x 10 m/s.
2. The ramp should be 58.4 m long.
3. The contestants on the survival s
Physics 120 Spring 2008 Answers to Problem Set 3
1. The final temperature of the instruments is about 27 C (or 300 K) just a few degrees above room temperature. They will be safe to touch.
2. (A) The total kinetic energy of the hollow sph
PHYSICS 120 PRINCIPLES OF PHYSICS I
1 LAB EXPERIMENT: MEASUREMENTS AND UNCERTAINTIES
Physics is an experimental science. No matter how elegant and compelling a theory may appear, its acceptance or rejection by the scientific com